Elastoplastic models represent an amorphous solid as being composed of cells, each of which may be thought of as representing a subvolume of the size of a plastic event. Each cell has a stress value, and a local yield stress value that is drawn from a distribution that forms part of the description of the model. A binary variable represents whether a plastic event is triggered at the cell or not. The stress at all sites increases monotonically with time with the increase of strain (typically at a fixed strain rate). A plastic event is triggered when the stress at a given site exceeds the local yield stress at that site. The stress then is propagated to other sites according to the propagator discussed earlier (or simpler ones) at a specified rate, and it relaxes at the site of the plastic events. Many variations of this basic strategy can be considered, including varying rates at which a plastic event is triggered, inclusion of thermal activation, etc. The expected variation of stress at a given site is shown in Figure REF . In addition to the fully explicit models of the kind described, various works have also considered mean field versions, such as the Hebraud-Lequeux model. This model describes the time evolution of the distribution of local stresses, dependent on a parameter \(\alpha \)  that controls stress diffusion, in proportion to the number of sites that display plastic activity [1]}. One obtains a transition from Newtonian fluid behaviour at low shear rates to yield stress fluid behaviour obeying the Herschel-Bulkley constitutive law, as \(\alpha \)  is varied. Elastoplastic models have also been employed to study avalanches, correlated plastic events that occur in tandem, typically in the steady flow regime [2]}, [3]}. Avalanches in the steady state are relevant if one is interested in the dynamics of plasticity in that regime[4]} (for example, strain localisation, which we discuss in the next section), and has been of interest in the context of intermittent dynamics in earthquakes and other driven systems.
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